Problem: $ B = \left[\begin{array}{rrr}0 & 0 & 2 \\ 4 & 4 & 1 \\ 3 & 3 & 2\end{array}\right]$ $ A = \left[\begin{array}{r}-2 \\ 1 \\ -1\end{array}\right]$ Is $ B+ A$ defined?
In order for addition of two matrices to be defined, the matrices must have the same dimensions. If $ B$ is of dimension $( m \times  n)$ and $ A$ is of dimension $( p \times  q)$ , then for their sum to be defined: 1. $ m$ (number of rows in $ B$ ) must equal $ p$ (number of rows in $ A$ ) and 2. $ n$ (number of columns in $ B$ ) must equal $ q$ (number of columns in $ A$ Do $ B$ and $ A$ have the same number of rows? Yes Yes No Yes Do $ B$ and $ A$ have the same number of columns? No Yes No No Since $ B$ has different dimensions $(3\times3)$ from $ A$ $(3\times1)$, $ B+ A$ is not defined.